Related papers: On Spatial Point Processes with Uniform Births and…
We study a class of quantum Markov processes that, on the one hand, is inspired by the micromaser experiment in quantum optics and, on the other hand, by classical birth and death processes. We prove some general geometric properties and…
Given a birth-death process on $\mathbb {N}$ with semigroup $(P_t)_{t\geq0}$ and a discrete gradient ${\partial}_u$ depending on a positive weight $u$, we establish intertwining relations of the form ${\partial}_uP_t=Q_t\,{\partial}_u$,…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…
In this paper, we study the significance of ecological interactions and separation of birth and death dynamics in stochastic heterogeneous populations via general birth-death processes. Interactions can manifest through the birth dynamics,…
In this paper we consider the distribution of the location of the path supremum in a fixed interval for self-similar processes with stationary increments. To this end, a point process is constructed and its relation to the distribution of…
We consider Markov processes that alternate continuous motions and jumps in a general locally compact polish space. Starting from a mechanistic construction, a first contribution of this article is to provide conditions on the dynamics so…
In this article we study the long time behaviour of measure-valued birth and death processes in continuous time, where the dynamics between jumps are one-dimensional Markov processes including diffusion and jumps. We consider the three…
We study the dynamics of an infinite system of point particles of two types. They perform random jumps in $\mathbf{R}^d$ in the course of which particles of different types repel each other whereas those of the same type do not interact.…
The effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact…
We study a class of multi-species birth-and-death processes going almost surely to extinction and admitting a unique quasi-stationary distribution (qsd for short). When rescaled by $K$ and in the limit $K\to+\infty$, the realizations of…
We consider continuous-time birth-and-death dynamics in $\mathbb{R}^d$ that admit at least one infinite-volume Gibbs point process based on area interactions as a reversible measure. For a large class of starting measures, we show that the…
This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…
We present and analyse the nonlinear classical pure birth process $\mathpzc{N} (t)$, $t>0$, and the fractional pure birth process $\mathpzc{N}^\nu (t)$, $t>0$, subordinated to various random times, namely the first-passage time $T_t$ of the…
Self-exciting spatio-temporal point process models predict the rate of events as a function of space, time, and the previous history of events. These models naturally capture triggering and clustering behavior, and have been widely used in…
Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this…
Birth-death processes (BDPs) are continuous-time Markov chains that track the number of "particles" in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle…
We describe a new class of models of quantum space-time based on energetic causal sets and show that under natural conditions space-time emerges from them. These are causal sets whose causal links are labelled by energy and momentum and…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
We consider a family of random locations, called intrinsic location functionals, of periodic stationary processes. This family includes but is not limited to the location of the path supremum and first/last hitting times. We first show that…
We develop a theory of first passage processes in stochastic non-equilibrium systems of birth-death type using two closely related epidemiological models as examples. Our method employs the probability generating function technique in…